The depth of field is that axial distance in object space within which objects are in (acceptable) focus on the image plane.The circle of confusion CoC size is small enough in that specific image plane. That image plane has an object distance such that the CoC size is zero.

the farther we focus our lens, the larger the depth of field.

What is the difference between focusing at infinity and focusing at the hyperfocal length H?

If we focus on an object located at the hyperfocal length H, all the objects hanksfrom H/2 to "infinity" will be in acceptable focus on the image plane. How is that possible? At H, the circle of confusion is zero. What is the size of the circle of confusion for the object(s) that are at H/2? How about the CoC size for object(s) beyond H? How it is possible that the CoC size grows so insignificantly as we move away from H?

If we focus on an object at "infinity" everything behind that object will be in focus. How about everything before that object?

Where does "optical infinity" start? Some say it starts several focal lengths away. Sure, when each point on the object emits rays whose reciprocal vergence is close to zero (or negligible). What happens when the camera focus is set to infinity? Does the lens aperture change to a specific setting?

One of the important things to note is the use of the word "acceptable" in "acceptable focus". Normally "acceptable" means "looks fairly sharp" when viewing and 8x10 print from a close distance (maybe 12"). However what's acceptable for me may not be acceptable for you and what's acceptable in a small print may not be acceptable in a large print - and so on.

If you focus at H, then at H/2 and infinity the circle of confusion is that which you used to calculate H. H iis a function of the chosen COF. Conventionally, for full frame that's around 30 microns, for APS-C it's around 18 microns and for 4/3 sensors it's around 15 microns. These are the numbers that give you the "acceptable" focus range in "standard DOF calculations.

I'm not sure what you mean by "optical infinity" other than "far enough away that both the point and infinity are in acceptable focus". In that case it's the hyperfocal distance, H

Well, people talk about setting the camera to "infinity" and objects located at infinity.Infinity is a concept, not a physical location. Usually photographers mean that the image of the object forms on the back focal plane of the lens. That is where the image plane of best focus (zero CoC, in theory, neglecting diffraction), is located.

For instance, let's consider a lens of focal length f=50 mm. If an object is located at 10 meters, then that object is located at infinity. Another object at 24 meters is also at infinity. An object at 5 meters may be at infinity. Technically, the lens equation gives image planes that are at slightly different locations, but all very close to the back focal plane. The differences are negligible....Only an object that is an infinite distance far away will have its image form exactly at the back focal plane and will be imaged as a point ( a star, for instance).

1) What physically happens when we set the camera to infinity by turning the f/# knob?

2) The hyperfocal length H could be closer that "infinity": if the object is located at H (once we decide on the acceptable CoC size and calculate H), the image will be on a plane that is not necessarily on the back focal plane (that is what happens to objects at infinity).

(1) Well, you don't set the camera to infinity with the f/# knob, you set it with the focusing control. What that does is place the rear nodal point of the lens exactly one focal length away from the sensor, so for a 50mm lens it puts the rear nodal point 50mm in front of the sensor.

(2) Anything that's then closer than infinity will image slightly behind the sensor, but for small distances (a few microns) this won't really affect sharpness. Even points at infinity don't image to an infinitely small point due to diffraction effects. Anything at the hyperfocal distance will image behind the sensor, so that the cone of light coming from a point in that object will be the diameter of the circle of confusion as it crosses the plane of the sensor. Typically 30 microns for a full frame sensor using the "typical" DOF estimation parameters using a geometric optics approximation model.

If I understand the question correctly, the main reason to focus at H and not infinity is that it doubles the available DOF. At infinity, the DOF extends from infinity to a point closer to the lens and from infinity to more infinity (Cantor would be proud!) 8^), the DOF beyond infinity is wasted.

When focused at H, the DOF extends from H to a point closer to the camera and from H to infinity, giving you the maximum DOF that also includes infinity.

Hello KeithB,so far so good. If we focus at H and H=3 meters, then everything from 3 meters to "infinity will be in acceptable focus (once we have a priori decided on the max acceptable size of the circle of confusion).

If we focus at infinity, wherever infinity is relative to our singel converging lens (say infinity starts at 20 meters), we should get a DOF from 20 meter to a farther infinity position, say 100 meters.....What happens between 15 meters and 20 meters?

Also, how can we explain, conceptually, using the concept of circle of confusion, the reason why the hyperfocal length H gives a larger DOF?

If we focus at infinity, wherever infinity is relative to our singel converging lens (say infinity starts at 20 meters), we should get a DOF from 20 meter to a farther infinity position, say 100 meters.....What happens between 15 meters and 20 meters?

If we focus at infinity, i.e. set the focus scale to the infinity mark, we get a DOF from the hyperfocal distance to infinity. That is by definition.

Things at the limits of the DOF aren't in focus. They are within the limits of "acceptable defocus"

If we focus at some distance for which our standard DOF formula says everything from 20m to 100m will be in "acceptable focus", then stuff from 15m to 20m will look a little soft and stuff past 100m will look a little soft.

If we focus a lens at infinity, objects at closer distance within the depth of field will also look sharp. The distance at which the closest object still looks sharp is called the hyperfocal distance H.OK

In this situation, depth of field "beyond infinity" is wasted.

WHY WASTED? WE HAVE A DOF FROM H TO INFINITY....

If instead of focusing the lens at infinity, we focus it at the hyperfocal distance, the depth of field will now extend from 1/2 the hyperfocal distance to infinity, so we have now maximized our utilization of the available depth of field.

OK. BUT WHY SO? WHY DO WE GAIN THAT LITTLE EXTRA 1/2 THE HYPERFOCAL LENGTH TO THE HYPERFOCAL LENGTH OF DOF? Is there a circle of confusion (I am clear on what it is) argument to explain it?

I like to think of DOF as a fixed quantity (arbitrarily determined and varying with aperture) of, say, length X; the actual plane of best focus is somewhere within that X, maybe in the middle, maybe a bit off one way or the other, but by definition, you or the manufacturer has decided that everything within the DOF is equally in focus - "acceptable".

When you focus at infinity you put the plane of best focus at "infinity" (this is not mathematical infinity, it is a property of the lens that simply means some physical limit and everything beyond it.) When you do this roughly half of your DOF is at "infinity" because it's all the same, and half is in front of it, the same as it is at all focus distances - you've discarded half of your DOF.

When you focus at the hyperfocal distance that includes infinity for a given aperture, you put the plane of best focus closer than infinity and the far limit of DOF at "infinity" (again, some distance that is a physical property of the lens and all beyond). You've maximized your DOF.

Keith, as you show in the diagram, the point H is like any other point: best focus at H (smallest CoC). The front point, at H/2, has the max circle of confusion and the rear limit of the DOF is at infinity.

Any other point that we focus on, other than H, has the front limit of the DOF and the rear limit of the DOF as finite points. So the hyperfocal point H is a special point. What makes it so special to have the rear limit of the DOF at infinity?

Sure, if you focus at infinity, the rear limit of the DOF is at infinity. That seems we are throwing DOF away but there are other objects that are beyond that infinity point and are within the DOF. So, practically, we still have useful DOF beyond infinity...

So the hyperfocal point H is a special point. What makes it so special to have the rear limit of the DOF at infinity?

Because that's the definition of the hyperfocal distance. It's the distance at which the rear limit of DOF is at infinity.

When you calculate the hyperfocal distance you are calculating the distance at which the rear limit of the DOF is infinity. Thats the condition from which the HFD equation is derived.

The mathematics are such that when you focus at the HFD, the rear limit of the DOF is infinity and the near limit of the DOF is half the HFD. That's the whole point of calculating the HFD, so you know where to focus to have the maximum range (including infinity) within the DOF.